On the dynamics of magnetic wave in ferrites: Influence of damping and inhomogeneous exchange effects

•We investigate solution of a system that describes the propagation of short-waves in inhomogeneous Ferrites subjected to damping effects; indeed.•We propose an integrable coupled system that stands as a generalized dissipative KMM-system that is helpful in taking into account damping effects.•We show that by means of ultra-fast process assumption, the solution of the dissipative KMM-system of our interest is provided.•We determine an approximated solution to the system in which inhomogeneous exchange and damping effects are taken into account.•We discuss deeply the influence of inhomogeneous exchange effect on the dynamics of short-waves in ferrites.•We proceed to some numerical simulations to sustain analytical results. We investigate throughout this paper the contributions of the damping effects and inhomogeneous exchange on the propagation of magnetic waves in ferrites. Indeed, we focus our attention on a nonlinear evolution system derived by Kuetche and coworkers (2015 J. Magn. Magn. Mater. 374 1), that takes into account the contributions that we aim at studying. We first proceed by some analytical analysis of the contribution of damping effects on the solutions to the system of our interest and after, the contribution of the inhomogeneous exchange, to unearth analytical expression of a solution that well approximates the above mentioned global system. It appears as a result that contribution of damping reduces the amplitude of waves during its motion. We unearth two types of inhomogeneities that effects act on the waves in different manner by increasing or decreasing the width of the soliton in ferrites. For ferrites made of poly-crystals in which involves the two types of inhomogeneities appearing periodically, wave moving therein will breath as it moves and there must be a case in which the two types of inhomogeneities can be combined in such a way to reduce their effects on the dynamics of the wave. We confirm the validity of the analytical analysis carried out by proceeding to some numerical simulations.